WASHINGTON — Sen. Lindsey Graham, R-S.C., an outspoken critic of defense secretary nominee Chuck Hagel, said Sunday that Hagel assuaged his concerns over an an alleged 2007 remark about Israel, while another detractor, Sen. John McCain, R-Ariz., said he expected his former colleague to ultimately win approval from the Senate.

Graham said on “Fox News Sunday” that Hagel sent him a letter disavowing an alleged comment about Israel and the State Department. A 2007 blog post from a GOP strategist resurfaced last week, indicating that Hagel remarked in an appearance that year at Rutgers University that the State Department had become adjunct to the Israeli Foreign Minister’s office.

“I got a letter back from Senator Hagel in response to my question, did you say that, and do you believe that? And the letter said he did not recall saying that. He disavows that statement,” Graham said.

Barring new developments, Graham said, Hagel’s explanation is satisfactory. “I’ll just take him at his word unless something new comes along,” he said.

McCain, who like Graham voted to block Hagel’s nomination process last week, said he expects the former Nebraska senator to win approval from the Senate, which is set to vote on him again later this month.

“I don’t believe he is qualified. But I don’t believe that we should hold up his nomination any further,” McCain said on NBC News’s “Meet The Press.”

The latest remarks from McCain and Graham illustrate the trajectory of the Senate battle over President Barack Obama’s nominee to head the Pentagon. While Republicans launched a historic filibuster last week and largely remain opposed to confirming Hagel, they’re willing to eventually allow a simple-majority vote on his nomination, virtually assuring him of approval, given Democrats’ Senate majority.

Calling for more time to review Hagel’s record, Graham and McCain were joined by all but four of their GOP colleagues last Thursday in a vote that prevented Hagel’s nomination from proceeding to a simple-majority vote. Democrats swiftly criticized the maneuver, which represented the first time a defense secretary nominee had been filibustered.

A top Obama administration official and a Senate Democratic ally sought to defend Hagel’s record on Sunday. White House Chief of Staff Denis McDonough said on “Meet The Press” that there is no undisclosed information about Hagel that would hurt his reputation. Sen. Jack Reed, D-R.I., vouched for Hagel’s credentials in an appearance on CNN’s “State of The Union,” saying he has “the experience” to be defense secretary, citing his status as a combat veteran, “a business leader” and “the second deputy head of V.A. in the Reagan administration.” Hagel, Reed noted, also has “the confidence of the president.”

Even as they are set to clear the way for Hagel’s confirmation, Republicans aren’t backing away from their highly critical assessment of him. Graham called Hagel “one of the most unqualified, radical choices for secretary of defense in a very long time.”

The Senate is set to vote on Hagel again on Feb. 26. If he is confirmed, it will bring to a close a process that exposed the sharp political divisions that have seized the Senate, and the persisting tension between the Obama administration and congressional Republicans on some national security issues.

Both Graham and McCain reiterated Sunday that they continue to have questions about the administration’s response to the Sept. 11, 2012, attack on a diplomatic outpost in Benghazi, Libya, that claimed the lives of four Americans, including Ambassador Christopher Stevens. Last week, Graham said that he didn’t think the Senate should move ahead on the nominations of Hagel for the Defense Department and John Brennan to head the Central Intelligence Agency until the administration was more forthcoming on the attack.

For his part, McDonough said he remains confident that Hagel will be a great defense secretary once he is confirmed, even as his nomination has sparked an intense political fight.

“He’s not going to be a weaker defense secretary. I think he’ll be a great defense secretary,” McDonough said.